Lang Moritz, Waldherr Steffen, Allgöwer Frank
Institute for Systems Theory and Automatic Control, Universität Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany.
PMC Biophys. 2009 Nov 17;2(1):10. doi: 10.1186/1757-5036-2-10.
Intrinsic noise is a common phenomenon in biochemical reaction networks and may affect the occurence and amplitude of sustained oscillations in the states of the network. To evaluate properties of such oscillations in the time domain, it is usually required to conduct long-term stochastic simulations, using for example the Gillespie algorithm. In this paper, we present a new method to compute the amplitude distribution of the oscillations without the need for long-term stochastic simulations. By the derivation of the method, we also gain insight into the structural features underlying the stochastic oscillations. The method is applicable to a wide class of non-linear stochastic differential equations that exhibit stochastic oscillations. The application is exemplified for the MAPK cascade, a fundamental element of several biochemical signalling pathways. This example shows that the proposed method can accurately predict the amplitude distribution for the stochastic oscillations even when using further computational approximations.PACS Codes: 87.10.Mn, 87.18.Tt, 87.18.VfMSC Codes: 92B05, 60G10, 65C30.
内在噪声是生化反应网络中的一种常见现象，可能会影响网络状态中持续振荡的发生和幅度。为了在时域中评估此类振荡的特性，通常需要进行长期随机模拟，例如使用 Gillespie 算法。在本文中，我们提出了一种无需长期随机模拟即可计算振荡幅度分布的新方法。通过该方法的推导，我们还深入了解了随机振荡背后的结构特征。该方法适用于表现出随机振荡的一大类非线性随机微分方程。以 MAPK 级联反应为例进行了应用，它是几种生化信号通路的基本组成部分。该示例表明，即使使用进一步的计算近似，所提出的方法也能准确预测随机振荡的幅度分布。物理和天文学分类号：87.10.Mn，87.18.Tt，87.18.Vf；数学学科分类号：92B05，60G10，65C30。
